430 lines
11 KiB
Plaintext
430 lines
11 KiB
Plaintext
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/*ident "@(#)complex.h 1.3 6/2/90" */
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#ifndef __COMPLEX_H
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#define __COMPLEX_H 1
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/*
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** (c) Copyright 1988-1990 by Dyad Software Corp.
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** All Rights Reserved
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**
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** Authors: lwd, geb
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*/
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#include <math.h>
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class ostream;
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class istream;
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class complex
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{
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public:
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friend double real ( const complex& );
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friend double imag ( const complex& );
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friend complex cos ( const complex& );
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friend complex cosh ( const complex& );
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friend complex sin ( const complex& );
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friend complex sinh ( const complex& );
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friend complex tan ( const complex& );
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friend complex tanh ( const complex& );
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friend complex log ( const complex& );
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friend complex log10 ( const complex& );
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friend complex sqrt ( const complex& );
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friend double abs ( const complex& );
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friend complex conj ( const complex& );
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friend double norm ( const complex& );
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friend double modulus ( const complex& );
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friend double arg ( const complex& );
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friend complex asin ( const complex& );
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friend complex acos ( const complex& );
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friend complex atan ( const complex& );
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friend complex asinh ( const complex& );
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friend complex atanh ( const complex& );
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friend complex exp ( const complex& );
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friend complex polar ( double r, double theta = 0);
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friend complex operator + ( const complex&, const complex& );
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friend complex operator + ( double, const complex& );
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friend complex operator + ( const complex&, double );
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friend complex operator - ( const complex&, const complex& );
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friend complex operator - ( double, const complex& );
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friend complex operator - ( const complex&, double );
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friend complex operator * ( const complex&, const complex& );
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friend complex operator * ( double, const complex& );
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friend complex operator * ( const complex&, double );
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friend complex operator / ( const complex&, const complex& );
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friend complex operator / ( double, const complex& );
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friend complex operator / ( const complex&, double );
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friend complex pow( const complex& lhs, double rhs );
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friend complex pow( const complex& lhs, const complex & rhs );
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friend complex pow( double lhs, const complex & rhs);
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friend complex pow( const complex& lhs, int rhs);
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friend int operator && ( const complex&, const complex& );
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friend int operator && ( double, const complex& );
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friend int operator && ( const complex&, double );
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friend int operator || ( const complex&, const complex& );
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friend int operator || ( double, const complex& );
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friend int operator || ( const complex&, double );
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friend int operator != ( const complex&, const complex& );
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friend int operator != ( double, const complex& );
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friend int operator != ( const complex&, double );
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friend int operator == ( const complex&, const complex& );
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friend int operator == ( double, const complex& );
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friend int operator == ( const complex&, double );
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friend ostream& operator << ( ostream& s, const complex& x);
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friend istream& operator >> ( istream& s, complex& x);
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public:
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complex ( );
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complex ( double r, double i ); /* this is not declared (double r, double i = 0)
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to avoid implicit conversion. Binary operations
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are explicitly declared thus avoiding potential
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ambiguities. */
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complex ( const complex & );
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double& real ( );
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double& imag ( );
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complex& operator = ( const complex& );
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complex& operator = ( double );
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complex& operator += ( const complex& );
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complex& operator += ( double );
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complex& operator -= ( const complex& );
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complex& operator -= ( double );
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complex& operator *= ( const complex& );
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complex& operator *= ( double );
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complex& operator /= ( const complex& );
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complex& operator /= ( double );
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int operator ! () const;
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complex operator - () const;
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private:
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double re;
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double im;
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};
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inline complex::complex ( )
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{
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/* remove these comments for initialization to (0,0)
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re = im = 0;
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*/
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}
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inline complex::complex ( double r, double i ): re(r), im(i) {}
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inline complex::complex( const complex& z)
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{
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re = z.re;
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im = z.im;
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}
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inline double real ( const complex& z){ return z.re; }
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inline double imag ( const complex& z){ return z.im; }
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inline double& complex::real (){ return re; }
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inline double& complex::imag (){ return im; }
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/* operator + */
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inline complex operator + ( const complex& lhs, const complex& rhs )
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{
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return complex ( lhs.re + rhs.re, lhs.im + rhs.im );
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}
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inline complex operator + ( double lhs, const complex& rhs )
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{
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return complex ( lhs + rhs.re, rhs.im );
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}
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inline complex operator + ( const complex& lhs, double rhs )
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{
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return complex ( lhs.re + rhs, lhs.im );
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}
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/* operator - */
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inline complex operator - ( const complex& lhs, const complex& rhs )
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{
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return complex ( lhs.re - rhs.re, lhs.im - rhs.im );
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}
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inline complex operator - ( double lhs, const complex& rhs )
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{
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return complex ( lhs - rhs.re, - rhs.im );
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}
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inline complex operator - ( const complex& lhs, double rhs )
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{
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return complex ( lhs.re - rhs, lhs.im );
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}
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/* operator * */
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inline complex operator * ( const complex& lhs, const complex& rhs )
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{
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return complex ( lhs.re * rhs.re - lhs.im * rhs.im,
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lhs.re * rhs.im + lhs.im*rhs.re );
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}
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inline complex operator * ( double lhs, const complex& rhs )
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{
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return complex ( lhs * rhs.re, lhs * rhs.im );
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}
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inline complex operator * ( const complex& lhs, double rhs )
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{
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return complex ( lhs.re * rhs, lhs.im*rhs );
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}
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/* operator / */
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inline complex operator / ( const complex& lhs, double rhs )
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{
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return complex( lhs.re / rhs, lhs.im /rhs );
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}
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/* unary operators */
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inline complex complex::operator - ( ) const
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{
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return complex ( -re, -im );
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}
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inline int complex::operator ! ( ) const
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{
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return ( re == 0 ) && ( im == 0 ) ;
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}
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inline complex & complex::operator = ( const complex& z)
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{
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re = z.re;
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im = z.im;
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return *this;
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}
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inline complex & complex::operator = ( double x)
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{
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re = x;
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im = 0;
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return *this;
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}
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/* operator *= */
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inline complex & complex::operator *= ( const complex& z)
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{
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*this = *this * z;
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return *this;
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}
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inline complex & complex::operator *= ( double x )
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{
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re *= x;
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im *= x;
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return *this;
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}
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inline complex & complex::operator /= ( const complex& z)
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{
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*this = *this / z;
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return *this;
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}
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inline complex & complex::operator /= ( double x)
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{
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re /= x;
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im /= x;
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return *this;
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}
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inline complex & complex::operator += ( const complex& z)
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{
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re += z.re;
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im += z.im;
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return *this;
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}
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inline complex & complex::operator += ( double x)
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{
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re += x;
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return *this;
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}
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inline complex & complex::operator -= ( const complex& z)
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{
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re -= z.re;
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im -= z.im;
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return *this;
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}
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inline complex & complex::operator -= ( double x)
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{
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re -= x;
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return *this;
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}
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/* operator && */
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inline int operator && ( const complex & lhs, const complex & rhs )
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{
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return (( lhs.re != 0 ) || ( lhs.im != 0 )) &&
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(( rhs.re != 0 ) || ( rhs.im != 0 )) ;
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}
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inline int operator && ( double lhs, const complex & rhs )
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{
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return ( lhs != 0 ) && (( rhs.re != 0 ) || ( rhs.im != 0 )) ;
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}
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inline int operator && ( const complex & lhs, double rhs )
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{
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return (( lhs.re != 0 ) || ( lhs.im != 0 )) && ( rhs != 0 ) ;
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}
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/* operator || */
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inline int operator || ( const complex & lhs, const complex & rhs )
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{
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return (( lhs.re != 0 ) || ( lhs.im != 0 )) ||
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(( rhs.re != 0 ) || ( rhs.im != 0 )) ;
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}
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inline int operator || ( double lhs, const complex & rhs )
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{
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return ( lhs != 0 ) || (( rhs.re != 0 ) || ( rhs.im != 0 )) ;
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}
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inline int operator || ( const complex & lhs, double rhs )
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{
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return (( lhs.re != 0 ) || ( lhs.im != 0 )) || ( rhs != 0 );
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}
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/* operator != */
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inline int operator != ( const complex& lhs, const complex& rhs )
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{
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return ( lhs.re != rhs.re ) || ( lhs.im != rhs.im );
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}
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inline int operator != ( double lhs, const complex& rhs )
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{
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return ( lhs != rhs.re ) || ( 0 != rhs.im );
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}
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inline int operator != ( const complex& lhs, double rhs )
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{
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return ( lhs.re != rhs ) || ( lhs.im != 0 );
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}
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/* operator == */
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inline int operator == ( const complex& lhs, const complex& rhs )
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{
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return ( lhs.re == rhs.re ) && ( lhs.im == rhs.im );
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}
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inline int operator == ( double lhs, const complex& rhs )
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{
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return ( lhs == rhs.re ) && ( 0 == rhs.im );
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}
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inline int operator == ( const complex& lhs, double rhs )
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{
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return ( lhs.re == rhs ) && ( lhs.im == 0 );
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}
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inline double arg( const complex& z)
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{
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return atan2(z.im,z.re);
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}
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inline complex atanh( const complex& z)
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{
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complex iz(-z.im, z.re);
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complex ix = atan(iz);
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return complex ( ix.im, -ix.re);
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}
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inline complex asinh( const complex& z)
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{
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complex iz(-z.im, z.re);
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complex ix = asin(iz);
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return complex ( ix.im, -ix.re);
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}
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inline double norm( const complex& z)
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{
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return z.re*z.re + z.im*z.im;
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}
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inline double modulus( const complex& z)
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{
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return abs(z);
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}
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inline complex conj( const complex& z)
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{
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return complex( z.re, -z.im );
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}
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inline complex cos( const complex& z )
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{
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return complex( cos(z.re) * cosh( z.im ), -( sin( z.re) * sinh(z.im)));
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}
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inline complex cosh( const complex& z )
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{
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return complex ( cosh(z.re) * cos(z.im), sinh(z.re) * sin(z.im) );
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}
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inline complex sin( const complex& z )
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{
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return complex ( sin(z.re) * cosh(z.im), cos(z.re) * sinh(z.im) );
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}
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inline complex sinh( const complex& z )
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{
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return complex ( sinh(z.re) * cos(z.im), cosh(z.re) * sin(z.im) );
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}
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inline complex tan( const complex& z )
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{
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double x = 2*z.re;
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double y = 2*z.im;
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double t = 1.0/(cos(x) +cosh(y));
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return complex( t*sin(x), t*sinh(y) );
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}
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inline complex tanh( const complex& z )
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{
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double x = 2*z.re;
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double y = 2*z.im;
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double t = 1.0/(cosh(x) +cos(y));
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return complex( t*sinh(x), t*sin(y) );
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}
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inline complex exp( const complex& z )
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{
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double x = exp(z.re);
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return complex( x*cos(z.im), x*sin(z.im) );
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}
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inline complex log( const complex& z )
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{
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return complex( log( abs(z) ), arg( z ) );
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}
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inline complex log10( const complex& z )
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{
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return complex( 0.2171472409516259*log( norm(z) ), arg( z ) );
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}
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inline complex polar ( double r, double theta )
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{
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return complex ( r * cos(theta), r * sin(theta));
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}
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#endif
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